HB spectra contain less speech information, and elaborate operation on them could bring a computational burden, so a lightweight magnitude module [1]} is used. The HB spectrum \(\mathbf {S}^\text{HB}=\text{Cat}(\mathbf {S}^{\text{HB}}_{r},\mathbf {S}^{\text{HB}}_{i}) \in \mathbb {R}^{T\times 2F}\)  is firstly converted to \(|\mathbf {S}^\text{HB}|\)  and \(\mathbf {S}^\text{HB}_\text{phase}\) , where \(|\mathbf {S}^\text{HB}|=({\mathbf {S}^{\text{HB}~2}_r}+{\mathbf {S}^\text{\text{HB}~2}_i})^{0.5}\)  and \({\mathbf {S}^\text{HB}_\text{phase}}=\text{arctan}({\mathbf {S}^\text{HB}_i},{\mathbf {S}^\text{HB}_r})\)  are the magnitude and phase, \(\mathbf {S}^\text{HB}_r\)  and \(\mathbf {S}^\text{HB}_i\)  are the real and imaginary parts, \(T\)  and \(F\)  denote the number of frames and the STFT bins respectively. The magnitude is used as input to predict the mask \(\mathbf {M}^\text{HB}\) . And HBM consists of fully connecting (FC), GRUs and ReLU [2]}, as shown in Fig. REF . Finally, the HB enhanced result \(\mathbf {S}^{\text{HB}^{\prime }}\)  is obtained by the Mask Apply M as follow,
\(\mathbf {S}^{\text{HB}^{\prime }} = |\mathbf {S}^\text{HB}| \odot \sigma (\mathbf {M}^\text{HB}) \odot e^{j\mathbf {S}^\text{HB}_{\text{phase}}}\) 
